Long-wavelength Approximation Research Articles

SU(3) Topology of Magnon-Phonon Hybridization in 2D Antiferromagnets.

Magnon-phonon hybrid excitations are studied theoretically in a two-dimensional antiferromagnet with an easy axis normal to the plane. We show that two magnon bands and one phonon band are intertwined by the magnetoelastic coupling through a nontrivial SU(3) topology, which can be intuitively perceived by identifying a skyrmion structure in the momentum space. Our results are insensitive to lattice details and generally applicable to two-dimensional antiferromagnets. We show this by developing a continuum theory as the long-wavelength approximation to the tight-binding model. The theoretical results can be probed by measuring the thermal Hall conductance as a function of the temperature and the magnetic field. We envision that the magnetoelastic coupling in antiferromagnets can be a promising venue in search of various topological excitations, which cannot be found in magnetic or elastic models alone.

Relativistic and non-Gaussianity contributions to the one-loop power spectrum

We compute the one-loop density power spectrum including Newtonian and relativistic contributions, as well as the primordial non-Gaussianity contributions from fNL and gNL in the local configuration. To this end we take solutions to the Einstein equations in the long-wavelength approximation and provide expressions for the matter density perturbation at second and third order. These solutions have shown to be complementary to the usual Newtonian cosmological perturbations. We confirm a sub-dominant effect from pure relativistic terms, manifested at scales dominated by cosmic variance, but find that a sizable effect of order one comes from gNL values allowed by Planck-2018 constraints, manifested at scales probed by forthcoming galaxy surveys like DESI and Euclid. As a complement, we present the matter bispectrum at the tree-level including the mentioned contributions.

The effects of Joule heating and variable thermal conductivity on peristaltic pumping of Jeffrey nanofluid in the presence of heat transfer

AbstractThis investigation aims to study Hall's current effect on the peristaltic flow of a Jeffrey nanofluid with variable thermal conductivity in an inclined asymmetric channel. Joule heating and oblique magnetic field effects are taken into consideration. A system of ordinary differential equations is obtained under the approximation of low Reynolds number and long wavelength, which consists of momentum, energy, and concentration equations. The influences of penitent physical parameters on the distribution of velocity, temperature, and concentration have been discussed graphically. Streamline graphs are offered in the terminus, which elucidates the trapping bolus phenomenon. The resulting equations are solved numerically using the ND Solver technique. The thermal conductivity parameter causes the pressure gradient to increase while reducing the pressure rise. Our present model can be applied to physiological flow transportation in the veins with heat transfer.

Mathematical Analysis on an Asymmetrical Wavy Motion of Blood under the Influence Entropy Generation with Convective Boundary Conditions

In this article, we discuss the entropy generation on the asymmetric peristaltic propulsion of non-Newtonian fluid with convective boundary conditions. The Williamson fluid model is considered for the analysis of flow properties. The current fluid model has the ability to reveal Newtonian and non-Newtonian behavior. The present model is formulated via momentum, entropy, and energy equations, under the approximation of small Reynolds number and long wavelength of the peristaltic wave. A regular perturbation scheme is employed to obtain the series solutions up to third-order approximation. All the leading parameters are discussed with the help of graphs for entropy and temperature profiles. The irreversibility process is also discussed with the help of Bejan number. Streamlines are plotted to examine the trapping phenomena. Results obtained provide an excellent benchmark for further study on the entropy production with mass transfer and peristaltic pumping mechanism.

Understanding Beam-Induced Electronic Excitations in Materials.

Optical electronic absorption spectroscopy and corresponding selection rules have played a prominent role in the development of the theory of electronic structure of materials. In this work, we expand the modern toolbox of chemistry and materials science to include electron and ion microscopies and spectroscopies, allowing spatially resolved interrogation of materials' atomic and electronic structures by beams of charged particles. Specifically, we formulate and discuss the selection rules for electronic excitation due to the interaction between materials and beams of charged particles. We show that transition probabilities for point charge-induced electronic excitations depend strongly on the position of the externally charged particles and can significantly deviate from those derived from the electric dipole (long-wavelength) approximation. We present and implement expressions within the linear response time-dependent density functional theory (TD-DFT) framework for rates of transition between the ground and excited states induced by an external point charge. The point charge-induced transition rates for particular electronic excitations from linear response TD-DFT were validated through comparison to excited state populations from real time TD-DFT simulations following an impulsive point charge perturbation, then evaluated on a three-dimensional grid to map their spatial dependence for a small polybenzoid. This method, when combined with information about excited state energy gradients, represents a first step toward an ab initio framework for probing the structural response of materials under irradiation by charged particles resulting from inelastic scattering. Engineering electron beam interaction with matter to manipulate single atoms and localized electronic states offers a revolutionary new regime beyond laser excitation.

Peristaltic Flow with Heat Transfer on Sisko Fluid in a Ciliated Arteries

The flow of blood through arteries is an important physiological problem. In the present investigation, we carried out to study the peristaltic of non-Newtonian incompressible blood flow with heat transfer through ciliated arteries. The blood flow is characterized by the generalized Sisko model. The nonlinear partial differential equations of the problem are simplified by using an approximation of long wavelength and low Reynolds number. The differential equations are solved analytically by using the perturbation method. We find that Sisko fluid parameter and the power index effects the behavior of the velocity where the velocity increase in the arteries then decreases near the wall, but the Sisko parameter give opposite behavior where the velocity decrease then increases near the wall of arteries. The velocity increase in arteries with the increase of cilia length and elliptic path. The temperature profile increases then decreases near the wall of arteries with the increase of power index, Sisko fluid parameter and Grashof number, while the temperature decrease then increase near the wall with increase of Sisko parameter. The effect of increase in the cilia length give an increase of the temperature. The pressure gradient increases with the increase of power index and elliptic path, while the pressure gradient decrease with an increase of elliptic path, Sisko parameter. The pressure gradient increases and decreases in a different interval with the increase the cilia length. Our results are illustrated through a set of Figures.

Peristaltic propulsion of Jeffrey nano-liquid and heat transfer through a symmetrical duct with moving walls in a porous medium

In this article, a computational study has been performed on the peristaltic propulsion of nanofluid flow through a porous rectangular duct. A non-Newtonian fluid model, i.e. Jeffrey model is considered to examine the behavior of nanoparticles. A Cartesian coordinate system is adopted for the three-dimensional duct. Furthermore, the three-dimensional rectangular duct contains porous wavy walls. An approximation of long wavelength and small Reynolds number have been applied to formulate the governing equations of momentum, energy, continuity, and concentration equation. These resulting coupled partial differential equations are further solved using Homotopy perturbation method and Genetic algorithm with a combination of Nelder Mead method. The purpose of the Genetic algorithm and Nelder Mead method is to reduce the residual error. For this purpose, numerical comparison of residual error is presented with a Homotopy perturbation method.

Peristaltic Propulsion of Jeffrey Nanofluid with Thermal Radiation and Chemical Reaction Effects

In this article, we have studied non-uniform hemodynamic nanofluid flow in the presence of an external magnetic field. The fluid contains magnetized nanoparticles in the presence of thermal radiation and chemical reaction. The magnetic field plays an essential role in targeting drugs by magnetic nanoparticles (“ferrofluids”) for different kinds of diseases in a human body. The Jeffrey viscoelastic model is employed to simulate non-Newtonian characteristics. With an approximation of long wavelength and minimal Reynolds number, a mathematical formulation has been performed. Numerical and analytical simulation has been used to examine the role of all the emerging parameters. Individual cases for the Newtonian fluid, non-Newtonian, nanofluid, and base fluid, have been exhibited numerically. A magnificent graphical correlation is additionally given with recently obtained outcomes to show the validity of the present findings and methodology.

Low-energy optical phonons induce glassy-like vibrational and thermal anomalies in ordered crystals

It is widely accepted that structural glasses and disordered crystals exhibit anomalies in their thermal, mechanical and acoustic properties as manifestations of the breakdown of the long-wavelength approximation in a disordered dissipative environment. However, the same type of glassy-like anomalies (i.e. boson peak in the vibrational density of states (VDOS) above the Debye level, peak in the normalized specific heat at T ≃ 10 K etc) have been recently observed also in perfectly ordered crystals, including thermoelectric compounds. Here we present a theory that predicts these surprising effects in perfectly ordered crystals as a result of low-lying (soft) optical phonons. In particular, it is seen that a strong boson peak anomaly (low-energy excess of modes) in the VDOS can be due almost entirely to the presence of low-energy optical phonons, provided that their energy is comparable to that of the acoustic modes at the Brillouin zone boundary. The boson peak is predicted also to occur in the heat capacity at low T. In presence of strong damping (which might be due to anharmonicities in the ordered crystals), these optical phonons contribute to the low-T deviation from Debye’s T3 law, producing a linear-in-T behavior which is typical of glasses, even though no assumptions of disorder whatsoever are made in the model. These findings are relevant for understanding and tuning thermal transport properties of thermoelectric compounds, and possibly for the enhancement of electron–phonon superconductivity.

Experimental study of crack density influence on the accuracy of effective medium theory

SUMMARYEffective medium theory plays an important role in the characterization of fractured reservoirs. The main goal of this paper is to assess the accuracy of three classical effective medium theories (compliance-based non-interaction approximation, Hudson theory and anisotropic self-consistent approximation) and investigate their applicable frequency range. To evaluate the crack density limitation of these models, we construct a series of physical models with crack density varying from 0 to 12 per cent. To satisfy the long-wavelength approximation of effective medium theory, we consider a crack diameter and aperture of 3 and 0.12 mm, respectively. To study their appropriate high-frequency laboratory condition, we use the ultrasonic transmission method to measure the elastic wave velocities at frequencies of 500, 250 and 100 kHz. The experimental results are then compared with the effective medium theories to discuss their accuracy. We also highlight and compare the accuracy of these theories for the inversion procedure to quantify the crack density.

Second-order homogenization of boundary and transmission conditions for one-dimensional waves in periodic media

We consider the homogenized boundary and transmission conditions governing the mean-field approximations of 1D waves in finite periodic media within the framework of two-scale analysis. We establish the homogenization ansatz (up to the second order of approximation), for both types of problems, by obtaining the relevant boundary correctors and exposing the enriched boundary and transmission conditions as those of Robin type. Rigorous asymptotic analysis is performed for boundary conditions, while the applicability to transmission conditions is demonstrated via numerical simulations. Within this framework, we also propose an optimized second-order model of the homogenized wave equation for 1D periodic media, that follows more accurately the exact dispersion relationship and generally enhances the performance of second-order approximation. The proposed analysis is applied toward the long-wavelength approximation of waves in finite periodic bilaminates, subject to both boundary and transmission conditions. A set of numerical simulations is included to support the mathematical analysis and illustrate the effectiveness of the homogenization scheme.

Multipole decompositions for directional light scattering

Applications of the multipole decomposition method for investigations of directional light scattering by a single nanoparticle and nanoparticle structures located in a finite spatial region are discussed. It is shown that, even in the case of relatively large scatterers, the multipole decomposition obtained in the long-wavelength approximation (LWA) may provide much better convergence than the multipole decomposition with the exact multipoles obtained from the spherical harmonics expansion. For an explanation of this seeming paradox, we derive in real space the exact multipole decomposition based on the spherical harmonics, presenting exact expressions for multipoles up to the electric 16-pole. Results obtained with the exact and approximate multipole expressions are discussed and compared. It is shown that for shape-anisotropic finite-size scatterers with different geometrical dimensions (like plates, rods, disks, rings, etc.), the required number of approximate multipoles providing accurate results may be much smaller than the required number of exact multipoles. For applicability of the LWA multipole decomposition, the only important parameter is the small ratio of the scatter size (its projection) in the scattering direction to the light wavelength. If this condition is fulfilled, the multipole decomposition with a small number of LWA multipoles is simpler than that based on the exact multipoles.

Influence of metachronal wave on hyperbolic tangent fluid model with inclined magnetic field

The purpose of this paper is to discuss the theoretical study of a nonlinear problem of cilia induced flow by considering the fluid as anincompressible non-Newtonian fluid (hyperbolic tangent fluid) model by means of ciliated walls. The leading equations of present flow problem are simplified under the consideration of long-wavelength approximation. We have utilized regular perturbation technique to solve the simplified leading equations of hyperbolic tangent fluid model. The analytical solution is computed for stream function and numerical solution is computed for the rise in pressure. The characteristics of the ciliary system on tangent hyperbolic fluid are analyzed graphically and discussed in detail. It has been found that when [Formula: see text], the results of pressure rise coincide with the results of Newtonian fluid. It has also been observed that the size of the trapping bolus decreases with an increase in Hartmann number and Weissenberg number.

Dual-polarized all-angle cloaking of a dielectric nanowire by helical graphene ribbons

Scattering from a dielectric nanowire coated by helical graphene strips (nanoribbons) is investigated for dual-polarized wave at oblique incidence. In the long-wavelength approximation, the helical strips are treated as a homogeneous layer with averaged tensor conductivity. It is shown that performance of well-known surface cloaks in the form of graphene monolayer, axial and azimuthal graphene strips can be deteriorated in a wide range of incidence angles. To overcome this problem, helical graphene strips are proposed as an advanced metasurface for dual-polarized all-angle cloaking of dielectric nanowire in the terahertz band. It is found that such metasurface suppresses scattering from nanowire more effectively as compared to graphene monolayer, regardless of the angle of wave incidence. Moreover, dual-polarized all-angle cloaking of dielectric nanowire can be broadly tuned in frequency with parameters of helical graphene strips.

Joint Effect of Magnetic Field and Heat Transfer on Particulate Fluid Suspension in a Catheterized Wavy Tube

The effect of wall slip conditions, porous media, and heat transfer on peristaltic inflow of MHD Newtonian fluid with suspended particles in a catheterized tube has been studied with long-wavelength and low-Reynolds number approximations. The analytical solution has been derived for velocity and temperature. The amplitude ratio, particle concentration, catheter size, and the dimensionless flow rate were used to discuss the pressure gradient. The solutions for velocity and temperature derived in the analysis have been computed numerically and investigated. The tube surface is maintained at a fixed temperature. The variations of physical variables with the pertinent parameters were discussed graphically. The mathematical model presented corresponds to the flow in the annular space between two concentric tubes. It has been deduced that the thermal energy is reduced with particles’ concentration and with slip condition through the catheterized tube. The flow accelerates with the magnetic field and slip condition at the wall, whereas it decreases at the catheter. The catheter size has a different effect on both pressure drop and friction force.

Homotopy perturbation method for peristaltic motion of gold-blood nanofluid with heat source

Purpose This paper aims to investigate the impacts of the gold nanoparticles on the peristaltic flow and heat transfer of blood in the presence of heat source. This element has been chosen because on comparing with the other common nanoparticles, gold nanoparticles are preferred due to their unique properties in absorbing the temperature when a heat source exists. Design/methodology/approach On simplifying the governing equations under the assumption of long-wavelength and low-Reynolds number approximations, the resulted system has been solved by applying the homotopy perturbation method. Then, detailed physical discussion has been introduced through several plots while focusing on the consequences of the current results on the treatment of cancer. Findings The present results revealed that the heat source has a great effect on the blood velocity, blood temperature and concentration of the gold nanoparticles within the artery/vein cavity when represented as asymmetric channel. Moreover, the accuracy of the current solutions was validated through several plots of the remainder error for each studied phenomenon. Originality/value The current idea gives some light on the attempts of using the gold nanoparticles in the treatment of cancer and therefore may lead to possible applications for diagnosis/therapy of the human cancer. To the best of authors’ knowledge, this is novel, very efficient and applicable.

Solitary waves in a granular chain of elastic spheres: Multiple solitary solutions and their stabilities.

A granular chain of elastic spheres via Hertzian contact incorporates a classical nonlinear force model describing dynamical elastic solitary wave propagation. In this paper, the multiple solitary waves and their dynamic behaviors and stability in such a system are considered. An approximate KdV equation with the standard form is derived under the long-wavelength approximation and small deformation. The closed-form analytical single- and multiple-soliton solutions are obtained. The construction of the multiple-soliton solutions is analyzed by using the functional analysis. It is found that the multiple-soliton solution can be excited by the single-soliton solutions. This result is confirmed by the numerical analysis. Based on the soliton solutions of the KdV equation, the analytic solutions of multiple dark solitary waves are obtained from the original dynamic equation of the granular chain in the long-wavelength approximation. The stability of the single and multiple dark solitary wave solutions are numerically analyzed by using both split-step Fourier transform method and Runge-Kutta method. The results show that the single dark solitary wave solution is stable, and the multiple dark solitary waves are unstable.

Closed-form representation for equivalent electromagnetic parameters of biaxial anisotropic honeycomb absorbing materials

A closed-form representation for equivalent electromagnetic parameters (EEP) of biaxial anisotropic honeycomb absorbing materials (HAM) is proposed based on long-wavelength approximation. Considering the specific physical parameters such as the side length of aramid paper honeycomb, the thickness of aramid paper honeycomb, the thickness of absorbing coating and the height of honeycomb absorbing material, the closed-form representation for its equivalent electromagnetic parameter is established and obtained. The correctness and effectiveness of the closed-form representation are verified by numerical simulation and experimental tests. The numerical simulation uses the finite time domain difference method combined with the Nicholson–Ross–Weir (NRW) method. The EEP of the anisotropic HAM calculated by the closed-form representation are more accurate than obtained by the NRW method. The honeycomb absorbing material was prepared by the immersion process, and the reflectance measured by the free space method was consistent with the reflectance calculated by the closed-form representation proposed in this paper within 2–18 GHz. The proposed closed-form representation for equivalent electromagnetic parameter of biaxial anisotropic HAM shows the biaxial anisotropic characteristics of HAM. At the same time, the new model has the advantages of simple principle, convenient use, high precision and frequency bandwidth, which may provide more accurate theoretical guidance for the design of HAM.

On the application of the Green‒Nagdi equations for the simulation of wave flows with undular bores

The basic conservation laws in the Green–Nagdi model of shallow-water theory are derived from the two-dimensional integral conservation laws of mass and the total momentum describing the plane-parallel flow in an ideal incompressible fluid above a horizontal bottom. This conclusion is based on the concept of a local hydrostatic approximation, which generalizes the concept of the long-wavelength approximation and is used for analyzing the applicability of the Green–Nagdi equations in modeling the wave flows with undular bores.

Dispersion of Surface Waves at the Interface between a Dielectric and a Finely Layered Ferrite–Graphene Medium

The propagation of guided ТМ- and ТЕ-polarized waves along the interface between a dielectric and a finely layered ferrite–graphene plasmon-polariton medium have been investigated. Based on the long-wavelength approximation, expressions for effective permittivity and permeability of a layered medium have been derived and used to establish dispersion relations for these waves and build frequency dependences of propagation constant real and imaginary parts. Where the waves are surface or radiation have been determined.